Question

Let us assume that there are two identical conducting spheres M and N that have charges ${{q}_{m}}$ and ${{q}_{n}}$ respectively. Let a third similar neutral sphere, P , be brought in contact with M and then separated. Now sphere P is brought in contact with N and then it is made separated. Then what will be the final charge on sphere P?
$\begin{align}
  & A.\dfrac{{{q}_{m}}+2{{q}_{n}}}{6} \\
 & B.\dfrac{{{q}_{m}}+{{q}_{n}}}{4} \\
 & C.{{q}_{m}}+\dfrac{{{q}_{n}}}{4} \\
 & D.\dfrac{{{q}_{m}}+2{{q}_{n}}}{4} \\
\end{align}$

Answer 1

Hint: First of all find the charge acquired by the sphere P when kept in contact with the sphere M. initially the charge on the sphere P will be zero. Then calculate the charge acquired by the sphere P when kept in contact with the sphere N. this time the initial charge will become equal to the charge acquired by the sphere P when kept in contact with sphere M.

Complete step by step solution:
The charge on the sphere M has been given as ${{q}_{m}}$ and the charge on the sphere N has been given as ${{q}_{n}}$.
When the sphere P is brought in contact with the sphere M, then the charge on P will become,
${{q}_{p}}=\dfrac{0+{{q}_{m}}}{2}$
Initially the charge of the sphere P will be zero.
After making the two spheres to be in contact, the charge on the sphere P will become,
${{q}_{p}}=\dfrac{{{q}_{m}}}{2}$
Now the sphere P is brought in contact with N the amount charge will get varied in both the spheres. During this process initially the sphere P will be having a charge mentioned as,
${{q}_{p}}=\dfrac{{{q}_{m}}}{2}$
And initially the charge in the sphere N will be mentioned as ${{q}_{n}}$.
Therefore after making these sphere in contact, the charge on the sphere P will become,
${{{q}'}_{p}}=\dfrac{\dfrac{{{q}_{m}}}{2}+{{q}_{n}}}{2}$
Simplifying this will give,
${{{q}'}_{p}}=\dfrac{{{q}_{m}}+2{{q}_{n}}}{4}$
Therefore the final charge on the sphere will become,
${{{q}'}_{p}}=\dfrac{{{q}_{m}}+2{{q}_{n}}}{4}$
Hence the answer for the question has been calculated.

This answer has been given as option D.

Note:
Electric charge is defined as the basic physical characteristic of matter that will cause it to experience a force if it is placed in an electromagnetic field. There are two kinds of electric charges. One is classified as positive and the other is as negative.